Imbalance compensation and automatic balancing in magnetic bearing systems using the Q-parameterization theory

Rotor imbalance leads to sinusoidal disturbance forces which cause undesirable vibration. The problem is addressed using actively controlled magnetic bearing systems. First, the dynamics of the magnetic bearing are described in state space form using airgap displacement. Velocity and airgap flux as state variables. Second, the system, which is unstable in nature, is stabilized using the Q-parameterization theory. In order to compensate for the imbalance disturbance forces, the controller Q-parameter is chosen such that rejection of sinusoidal disturbances is achieved. In order to achieve automatic balancing, the imbalance is assumed as a sinusoidal noise in the measured signal, and the controller 4-parameter is chosen such that rejection of sinusoidal noise is achieved. In both cases the frequency of the sinusoidal disturbance/noise is assumed to be equal to the rotational speed. Simulation results are presented and show the robustness of the proposed controllers and that the rejection of sinusoidal disturbances is achieved. Also rotation of tile rotor around its axis of inertia is achieved.